Regarding havesting - I like them quite mature, when the skin is very hard and doesn't dent when you really push your thumbnail into it, the flesh by then has started to pick up a yellowish tinge, and the flavour and texture is a slightly 'mealy'. My spouse likes them younger, once they've just stopped growing, but whilst the skin is still soft, and the flesh is more of a courgette-green. Each to his own I suppose, although 'young' gems won't keep for long once the season ends.
I don't find that taking young and old squash from the same plant a problem.
I let the plants have as much space as I can (although next year I'm going to try and grow them up pyramids maintain yield in a more confined area, but this might not be too successful because the plants then won't be able to 'root' along their length and so will take up less nutrients). I just hack them back once they start to take over inappropriate parts of the garden. I've got half a dozen plants in about 20 square m. I've never bothered with restricting the number of squash during the growing season.
They stay in the ground until the first frosts, but by then they're usually suffering from powdery mildew (but still cropping). I expect to get about 20 squash from each plant. They are also great at keeping down the weeds!
Because the variety that I was sent seems to take root along its length I think of each of my gem squash plants as being like a 'colony', so provided it's well fed mine are quite happy to produce lots of quality fruit. These 'extra' roots are one of the reasons that I like to provide a decent mulch for them to get stuck in to.
I do plant them in a lot of compost - say 100l per plant, mulch once they become established (at least 10cm of well rotted straw/stable manure) and, and give them a foliar feed every couple of weeks once they start flowering - either tomato or seaweed.
I provide them with plenty of water at ground level (leaky hose), although thais hasn't been needed this year.
Since starting to grow them 4 years ago I have never had problems with slugs, birds, or any other bug. If all plants were as easy.
What I've not been able to do is grow a decent butternut...grrrr